On suspension flow in a porous medium

Abstract

The phenomenon of suspension flow in porous medium is accompanied by the time-space change of the concentration N of solid particles suspended in dispersing fluid, as well as by the change of the concentration P of particles deposited (trapped) in porous medium. These changes are due to the trapping of suspended particles by porous medium i.e. to the, so-called, colmatage phenomenon, as well as due to the breaking away of particles of this medium i.e. to the, so-called, scouring phenomenon. The system of the equations, which describes the transport of the volume of suspended particles and the kinetics of the colmatage-scouring process, determines the functions N and P. In the equation describing the transport phenomenon there is taken into account the phenomenon of diffusion of particles suspended in dispersing fluid. The kinetics equation of the colmatage-scouring has been obtained by averaging the stochastic process (of a ‘birth-death’ type) assumed as the mathematical model of the phenomenon concerned. If the diffusion effect is neglected the mathematical model comes to a system of hyperbolic equations. There has been obtained a particular solution of this system important from the point of view of experimental investigations. In particular, the case of colmatage phenomenon due to the impulse inject of suspension is interesting. The characteristics of the system of equations mentioned above form the lines along which the discontinuities of boundary—initial conditions are propagating. The experiments show the effect of a wash-out of these discontinuities. This suggests the consideration of a system of equations in which the diffusion effect is taken into account. The consideration of this diffusion effect leads to a non-linear parabolic equation. The particular solution of this equation has been obtained for certain boundary-initial conditions. The solution of Cauchy's problem related to the colmatage-scouring phenomenon is interesting from the point of view of experimental investigations. The basic solution of this problem describes the colmatage-scouring phenomenon due to the initial condition in the form of an impulse inject.